So I some how stumbled into Likkin-Na and am now completely stuck. I don't have the air teleport or many other skills that are necessary for this section. So my question is how the hell do I get out of here?

Gallery

I can pass though single walls but they have to be on the same level as myself (which none of them are of course). Attached is the map and my skills.

Update: In that area there was a little glitch that show I had been somewhere when I actually had not. I now have the Brown Coat and am running around. The one upgrade I really need now is the 'Warp to your drone' upgrade.